Addendum to “Limit Sets of Typical Homeomorphisms”
Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 240-244
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Given an integer $n\,\ge \,3$ , a metrizable compact topological $n$ -manifold $X$ with boundary, and a finite positive Borel measure $\mu$ on $X$ , we prove that for the typical homeomorphism $f:\,X\,\to \,X$ , it is true that for $\mu$ -almost every point $x$ in $X$ the restriction of $f$ (respectively of ${{f}^{-1}}$ ) to the omega limit set $\omega \left( f,\,x \right)$ (respectively to the alpha limit set $\alpha \left( f,\,x \right)$ ) is topologically conjugate to the universal odometer.
Mots-clés :
37B20, 54H20, 28C15, 54C35, 54E52, topological manifolds, homeomorphisms, measures, Baire category, limit sets
Jr., Nilson C. Bernardes. Addendum to “Limit Sets of Typical Homeomorphisms”. Canadian mathematical bulletin, Tome 57 (2014) no. 2, pp. 240-244. doi: 10.4153/CMB-2012-033-1
@article{10_4153_CMB_2012_033_1,
author = {Jr., Nilson C. Bernardes},
title = {Addendum to {{\textquotedblleft}Limit} {Sets} of {Typical} {Homeomorphisms{\textquotedblright}}},
journal = {Canadian mathematical bulletin},
pages = {240--244},
year = {2014},
volume = {57},
number = {2},
doi = {10.4153/CMB-2012-033-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-033-1/}
}
TY - JOUR AU - Jr., Nilson C. Bernardes TI - Addendum to “Limit Sets of Typical Homeomorphisms” JO - Canadian mathematical bulletin PY - 2014 SP - 240 EP - 244 VL - 57 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2012-033-1/ DO - 10.4153/CMB-2012-033-1 ID - 10_4153_CMB_2012_033_1 ER -
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